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Volume Title: NBER Macroeconomics Annual 2003, Volume 18 Volume Author/Editor: Mark Gertler and Kenneth Rogoff, editors Volume Publisher: The MIT Press Volume ISBN: 0-262-07253-X Volume URL: http://www.nber.org/books/gert04-1 Conference Date: April 4-5, 2003 Publication Date: July 2004

Title: Disagreement about Inflation Expectations Author: N. Gregory Mankiw, Ricardo Reis, Justin Wolfers URL: http://www.nber.org/chapters/c11444

N. Gregory Mankiw, Ricardo Reis, and Justin Wolfers HARVARD UNIVERSITY AND NBER; HARVARD UNIVERSITY; AND STANFORD UNIVERSITY AND NBER

Disagreement About Inflation Expectations 1. Introduction At least since Milton Friedman's renowned presidential address to the American Economic Association in 1968, expected inflation has played a central role in the analysis of monetary policy and the business cycle. How much expectations matter, whether they are adaptive or rational, how quickly they respond to changes in the policy regime, and many related issues have generated heated debate and numerous studies. Yet throughout this time, one obvious fact is routinely ignored: not everyone has the same expectations. This oversight is probably explained by the fact that, in much standard theory, there is no room for disagreement. In many (though not all) textbook macroeconomic models, people share a common information set and form expectations conditional on that information. That is, we often assume that everyone has the same expectations because our models say that they should. The data easily reject this assumption. Anyone who has looked at survey data on expectations, either those of the general public or those of professional forecasters, can attest to the fact that disagreement is substantial. For example, as of December 2002, the interquartile range of inflation expectations for 2003 among economists goes from V/2% to 2Vi%.

We would like to thank Richard Curtin and Guhan Venkatu for help with data sources, and Simon Gilchrist, Robert King, and John Williams for their comments. Doug Geyser and Cameron Shelton provided research assistance. Ricardo Reis is grateful to the Fundacao Ciencia e Tecnologia, Praxis XXI, for financial support.

210 • MANKIW, REIS, & WOLFERS Among the general public, the interquartile range of expected inflation goes from 0% to 5%. This paper takes as its starting point the notion that this disagreement about expectations is itself an interesting variable for students of monetary policy and the business cycle. We document the extent of this disagreement and show that it varies over time. More important, disagreement about expected inflation moves together with the other aggregate variables that are more commonly of interest to economists. This fact raises the possibility that disagreement may be a key to macroeconomic dynamics. A macroeconomic model that has disagreement at its heart is the stickyinformation model proposed recently by Mankiw and Reis (2002). In this model, economic agents update their expectations only periodically because of the costs of collecting and processing information. We investigate whether this model is capable of predicting the extent of disagreement that we observe in the survey data, as well as its evolution over time. The paper is organized as follows. Section 2 discusses the survey data on expected inflation that will form the heart of this paper. Section 3 offers a brief and selective summary of what is known from previous studies of survey measures of expected inflation, replicating the main findings. Section 4 presents an exploratory analysis of the data on disagreement, documenting its empirical relationship to other macroeconomic variables. Section 5 considers what economic theories of inflation and the business cycle might say about the extent of disagreement. It formally tests the predictions of one such theory—the sticky-information model of Mankiw and Reis (2002). Section 6 compares theory and evidence from the Volcker disinflation. Section 7 concludes.

2. Inflation Expectations Most macroeconomic models argue that inflation expectations are a crucial factor in the inflation process. Yet the nature of these expectations—in the sense of precisely stating whose expectations, over which prices, and over what horizon—is not always discussed with precision. These are crucial issues for measurement. The expectations of wage- and price-setters are probably the most relevant. Yet it is not clear just who these people are. As such, we analyze data from three sources. The Michigan Survey of Consumer Attitudes and Behavior surveys a cross section of the population about their expectations over the next year. The Livingston Survey and the Survey of Professional Forecasters (SPF) covers more sophisticated analysts—economists working

Disagreement About Inflation Expectations • 211

Table 1 SURVEYS OF INFLATION EXPECTATIONS Survey of professional forecasters

Michigan survey

Livingston survey

Survey population

Cross section of the general public

Academic, business, finance, market, and labor economists

Market economists

Survey organization

Survey Research Center, University of Michigan

Originally Joseph Livingston, an economic journalist; currently the Philadelphia Fed

Originally ASA/NBER; currently the Philadelphia Fed

Average number of respondents

Roughly 1000-3000 per quarter to 1977, then 500-700 per month to present

48 per survey (varies from 14-63)

34 per survey (varies from 9-83)

Starting date

Qualitative questions: 1946 Ql1; quantitative responses: January 1978

1946, first half (but the early data is unreliable)1

GDP deflator: 1968,

Periodicity

Most quarters from 1947 Ql to 1977 Q4; every month from January 1978

Semi-annual

Quarterly

Inflation expectation

Expected change in prices over the next 12 months

Consumer Price Index (this quarter, in 2 quarters, in 4 quarters)

GDP deflator level, quarterly CPI level (6 quarters)

Q4;

CPI inflation: 1981, Q3

1. Our quantitative work focuses on the period from 1954 onward.

in industry and professional forecasters, respectively. Table 1 provides some basic details about the structure of these three surveys.1 Although we have three sources of inflation expectations data, throughout this paper we will focus on four, and occasionally five, series. Most papers analyzing the Michigan data cover only the period since 1978, during which these data have been collected monthly (on a relatively consistent basis), and respondents were asked to state their precise quantitative 1. For more details about the Michigan Survey, the Livingston Survey and the SPF, see Curtin (1996), Croushore (1997), and Croushore (1993), respectively.

212 • MANKIW, REIS, & WOLFERS Figure 1 MEDIAN INFLATION EXPECTATIONS AND ACTUAL INFLATION Michigan Survey

Michigan Experimental

Livingston

SPF: GDP Deflator

15-1 10-

0-

15-

1950

1960

1970

1980

1990

2000 1950

1960

1970

1980

1990

2000

Year: Actual and forecast shown at endpoint of horizon Year-ended inflation rate

Expected Inflation

inflation expectations. However, the Michigan Survey of Consumer Attitudes and Behaviors has been conducted quarterly since 1946, although for the first 20 years respondents were asked only whether they expected prices to rise, fall, or stay the same. We have put substantial effort into constructing a consistent quarterly time series for the central tendency and dispersion of inflation expectations through time since 1948. We construct these data by assuming that discrete responses to whether prices are expected to rise, remain the same, or fall over the next year reflect underlying continuous expectations drawn from a normal distribution, with a possibly time-varying mean and standard deviation.2 We will refer to these constructed data as the Michigan experimental series. Our analysis of the Survey of Professional Forecasters will occasionally switch between our preferred series, which is the longer time series of forecasts focusing on the gross domestic product (GDP) deflator (starting in 1968, Q4), and the shorter consumer price index (CPI) series (which begins in 1981, Q3). Figure 1 graphs our inflation expectations data. The horizontal axis refers to expectations at the endpoint of the relevant forecast horizon 2. Construction of this experimental series is detailed in the appendix, and we have published these data online at www.stanford.edu/people/jwolfers (updated January 13, 2004).


rather than at the time the forecast was made. Two striking features emerge from these plots. First, each series yields relatively accurate inflation forecasts. And second, despite the different populations being surveyed, they all tell a somewhat similar story. By simple measures of forecast accuracy, all three surveys appear to be quite useful. Table 2 shows two common measures of forecast accuracy: the square root of the average squared error (RMSE) and the mean absolute error (MAE). In each case we report the accuracy of the median expectation in each survey, both over their maximal samples and for a common sample (September 1982-March 2002). Panel A of the table suggests that inflation expectations are relatively accurate. As the group making the forecast becomes increasingly sophisticated, forecast accuracy appears to improve. However, Panel B suggests that these differences across groups largely reflect the different periods over which each survey has been conducted. For the common sample that all five measures have been available, they are all approximately equally accurate. Of course, these results reflect the fact that these surveys have a similar central tendency, and this fact reveals as much as it hides. Figure 2 presents simple histograms of expected inflation for the coming year as of December 2002. Here, the differences among these populations become starker. The left panel pools responses from the two surveys of economists and shows some agreement on expectations, with most respondents expecting inflation in the VA to 3% range. The survey of consumers reveals substantially greater disagreement. The interquartile range of consumer expectations stretches from 0 to 5%, and this distribution shows quite long tails, with 5% of the population expecting deflation, while 10% expect inflation of at Table 2 INFLATION FORECAST ERRORS Michigan

Michigan experimental

Livingston

SPF-GDP deflator

SPF-CPI

1954, Q42002, Q l 2.32% 1.77%

1954, H l 2001, H2 1.99% 1.38%

1969, Q42002, Q l 1.62% 1.22%

1982, Q 3 2002, Q l 1.29% 0.97%

1.10% 0.91%

1.29% 0.97%

Panel A: maximal sample Sample RMSE MAE

Nov. 1974May 2002 1.65% 1.17%

Panel B: common time period (September 1982-March 2002) RMSE MAE

1.07% 0.85%

1.24% 0.95%

1.28% 0.97%

214 • MANKIW, REIS, & WOLFERS least 10%. These long tails are a feature throughout our sample and are not a particular reflection of present circumstances. Our judgment (following Curtin, 1996) is that these extreme observations are not particularly informative, and so we focus on the median and interquartile range as the relevant indicators of central tendency and disagreement, respectively. The extent of disagreement within each of these surveys varies dramatically over time. Figure 3 shows the interquartile range over time for each of our inflation expectations series. A particularly interesting feature of these data is that disagreement among professional forecasters rises and falls with disagreement among economists and the general public. Table 3 confirms that all of our series show substantial co-movement. This table focuses on quarterly data—by averaging the monthly Michigan numbers and linearly interpolating the semiannual Livingston numbers. Panel A shows correlation coefficients among these quarterly estimates. Panel B shows correlation coefficients across a smoothed version of the data (a five-quarter centered moving average of the interquartile range). (The experimental Michigan data show a somewhat weaker correlation, particularly in the high-frequency data, probably reflecting measurement error caused by the fact that these estimates rely heavily on the proportion of the sample expecting price declines—a small and imprecisely estimated fraction of the population.) Figure 2 DISTRIBUTION OF INFLATION EXPECTATIONS Professional Economists

Consumers

Livingston Survey and SPF, Combined

Michigan Survey

m

Empirical Distribution

Empirical Distribution

—«• Kernel Density Estimate

10-

Kernel Density Estimate

10-

0- 1 0 1 2 3 4 Expected Inflation over the Year to December 2003, %

-5.0 -2.5 0.0 2.5 5.0 7.5 10.0 Expected Inflation over the Year to December 2003, % Expectations < -5% and > 10% truncated lo endpoints.

Disagreement About Inflation Expectations • 215 Figure 3 DISAGREEMENT OVER INFLATION EXPECTATIONS THROUGH TIME

Disagreement Among Consumers 10-

f 4H a

Michigan Experimental Series

Michigan Survey

2H

1950

1960

1970

1980

1990

2000

Year 2.5H

Disagreement Among Economists

S)2.0*15H

§1.0^0

o.oH 1950

Survey of Professional Forecasters 1960

1970

1980

Livingston Survey 1990

2000

1990

2000

Year

Inflation Rate 2

I

5i

o1950

1960

1970

1980 Year

Date reflects when the forecast is made.

216 • MANKIW, REIS, & WOLFERS Table 3 DISAGREEMENT THROUGH TIME: CORRELATION ACROSS SURVEYS1 Michigan experimental

Livingston

0.682 0.809

1.000 0.391

1.000

0.700 0.667

0.502 0.231

0.712 0.702

Michigan

SPF-GDP deflator

SPF-CPI

1.000 0.688

1.000

1.000 0.865

1.000

Panel A: actual quarterly data

Michigan Michigan experimental Livingston SPF-GDP deflator SPF-CPI

1.000

Panel B: 5 quarter centered moving averages

Michigan Michigan experimental Livingston SPF-GDP deflator SPF-CPI

1.000 0.729 0.869

1.000 0.813

1.000

0.850 0.868

0.690 0.308

0.889 0.886

1. Underlying data are quarterly. They are created by taking averages of monthly Michigan data and by linearly interpolating half-yearly Livingston data.

A final source of data on disagreement comes from the range of forecasts within the Federal Open Market Committee (FOMC), as published biannually since 1979 in the Humphrey-Hawkins testimony.3 Individuallevel data are not released, so we simply look to describe the broad pattern of disagreement among these experts. Figure 4 shows a rough (and statistically significant) correspondence between disagreement among policymakers and disagreement among professional economists. The correlation of the range of FOMC forecasts with the interquartile range of the Livingston population is 0.34, 0.54 or 0.63, depending on which of the three available FOMC forecasts we use. While disagreement among Fedwatchers rose during the Volcker disinflation, the range of inflation forecasts within the Fed remained largely constant—the correlation between disagreement among FOMC members and disagreement among professional forecasters is substantially higher after 1982. We believe that we have now established three important patterns in the data. First, there is substantial disagreement within both naive and expert 3. We are grateful to Simon Gilchrist for suggesting this analysis to us. Data were drawn from Gavin (2003) and updated using recent testimony published at http://www.federalreserve.gov/boarddocs/ hh/ (accessed December 2003).


populations about the expected future path of inflation. Second, there are larger levels of disagreement among consumers than exists among experts. And third, even though professional forecasters, economists, and the general population show different degrees of disagreement, this disagreement tends to exhibit similar time-series patterns, albeit of a different amplitude. One would therefore expect to find that the underlying causes behind this disagreement are similar across all three datasets.

3. The Central Tendency of Inflation Expectations Most studies analyzing inflation expectations data have explored whether empirical estimates are consistent with rational expectations. The rational expectations hypothesis has strong implications for the time series of Figure 4 DISAGREEMENT AMONG THE FOMC

Disagreement Through Time

5-Month Ahead Forecasts 3-

91 «NM)O

•so

• 96 Correlation (Whole Sample) = 0.54 Correlation (Post-1982) = 0.64

1980 1985 1990 1995 2000 Humphrey Hawkins Testimony Date

0

10-Month Ahead Forecasts

17-Month Ahead Forecasts

1 2 3 IQR of Livingston Forecasts (%)

83 ' *}

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88A84 A 93

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A9A82 80 A 0190 AA900 A 95 A96 A 97 Correlation (Whole Sample) = 0.34 Correlation (Post-1982) = 0.74

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jjo0

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1 2 IQR of Livingston Forecasts (%)

Humphrey-Hawkins testimony in February and July provides forecasts for inflation over the calendar year. Inflation concept varies.

218 • MANKIW, REIS, & WOLFERS expectations data, most of which can be stated in terms of forecast efficiency. More specifically, rational expectations imply (statistically) efficient forecasting, and efficient forecasts do not yield predictable errors. We now turn to reviewing the tests of rationality commonly found in the literature and to providing complementary evidence based on the estimates of median inflation expectations in our sample.4 The simplest test of efficiency is a test for bias: are inflation expectations centered on the right value? Panel A of Table 4 reports these results, regressing expectation errors on a constant. Median forecasts have tended to underpredict inflation in two of the four data series, and this divergence is statistically significant; that said, the magnitude of this bias is small.5 By regressing the forecast error on a constant and the median inflation expectation,6 panel B of the table tests whether there is information in these inflation forecasts themselves that can be used to predict forecasting errors. Under the null of rationality, these regressions should have no predictive power. Both the Michigan and Livingston series can reject a rationality null on this score, while the other two series are consistent with this (rather modest) requirement of rationality. Panel C exploits a time-series implication of rationality, asking whether today's errors can be forecasted based on yesterday's errors. In these tests, we regress this year's forecast error on the realized error over the previous year. Evidence of autocorrelation suggests that there is information in last year's forecast errors that is not being exploited in generating this year's forecast, violating the rationality null hypothesis. We find robust evidence of autocorrelated forecast errors in all surveys. When interpreting these coefficients, note that they reflect the extent to which errors made a year ago persist in today's forecast. We find that, on average, about half of the error remains in the median forecast. One might object that last year's forecast error may not yet be fully revealed by the time this year's forecast is made because inflation data are published with only one month lag. Experimenting with slightly longer lags does not change these results significantly.7 Finally, panel D asks whether inflation expectations take sufficient account of publicly available information. We regress forecast errors on recent macroeconomic data. Specifically, we analyze the inflation rate, the Treasury-bill rate, and the unemployment rate measured one month prior 4. Thomas (1999) provides a survey of this literature. 5. Note that the construction of the Michigan experimental data makes the finding of bias unlikely for that series. 6. Some readers may be more used to seeing regressions of the form n = a + bEt_12Kt, where the test for rationality is a joint test of a = 0 and b = 1. To see that our tests are equivalent, simply rewrite nt - Et_l2n, = a + (1 - b)E,_unt. A test of a = 0 and b = 1 translates into a test that the constant and slope coefficient in this equation are both zero. 7. Repeating this analysis with mean rather than median expectations yields weaker results.

Disagreement About Inflation Expectations • 219 Table 4 TESTS OF FORECAST RATIONALITY: MEDIAN INFLATION EXPECTATIONS1 Michigan Panel A: testing for bias: nt-Et_12nt

a: mean error (Constant only)

Michiganexperimental

Livingston

SPF (GDP deflator)

-0.09% (0.34)

0.63%** (0.30)

-0.02% (0.29)

=a

0.42% (0.29)

Panel B: Is information in the forecast fully exploited? nt - £f_12 nt = a + P i P: £,_12 [nt] a: constant Adj. R2 Reject eff.? a = p = 0 (p-value)

0.349** (.161) -1.016%* (.534) 0.197 Yes (p = 0.088)

-0.060 (.207) -0.182% (.721) -0.003 No (p = 0.956)

0.011 (.142) 0.595% (.371) -0.011 Yes (p = 0.028)

Panel C: Are forecasting errors persistent? nt - Et_u nt - a P: nt_u - E t _ 24 [rc,_12]

a: constant Adj. R2

0.371** (0.158) 0.096% (0.183) 0.164

a: constant

-0.816% (0.975) 0.801*** P : Ef-12 [nt] (0.257) y: inflation(_13 -0.218* (0.121) K: Treasury billt_13 -0.165** (0.085) 8: u n e m p l o y m e n t ^ 0.017 (0.126) Reject eff.? y = K = 8 = 0 Yes (p-value) (p = 0.049) Adjusted R2 0.293 Sample Periodicity N

Nov. 1974May 2002 Monthly 290

+ P (7if_12 - Et_24'i^-12)

.580*** (0.115) 0.005% (0.239) 0.334

Panel D: Are macroeconomic data fully exploited? nt

0.026 (.128) -0.132% (.530) -0.007 No (p = 0.969)

0.490*** (0.132) 0.302% (0.210) 0.231 -

Et_12%t

0.640*** (0.224) -0.032% (0.223) 0.375 = a

+

P £(_12 [7tJ

0.242% (1.143) -0.554*** (0.165) 0.610*** (0.106) -0.024 (0.102) -0.063 (0.156) Yes (p = 0.000) 0.382

4.424%*** (0.985) 0.295 (0.283) 0.205 (0.145) -0.319*** (0.106) -0.675*** (0.175) Yes (p = 0.000) 0.306

3.566%*** (0.970) 0.287 (0.308) 0.200 (0.190) -0.321*** (0.079) -0.593*** (0.150) Yes (p = 0.000) 0.407

1954, Q 4 2002, Q l Quarterly 169

1954, H l 2001, H2 Semiannual 96

1969, Q42002, Ql Quarterly 125

1. ***, ** and * denote statistical significance at the 1%, 5%, and 10% levels, respectively (Newey-West standard errors in parentheses; correcting for autocorrelation up to one year).

220 • MANKIW, REIS, & WOLFERS to the forecast because these data are likely to be the most recent published data when forecasts were made. We also control for the forecast itself, thereby nesting the specification in panel B of Table 4. One might object that using real-time data would better reflect the information available when forecasts were made; we chose these three indicators precisely because they are subject to only minor revisions. Across the three different pieces of macroeconomic information and all four surveys, we often find statistical evidence that agents are not fully incorporating this information in their inflation expectations. Simple bivariate regressions (not shown) yield a qualitatively similar pattern of responses. The advantage of the multivariate regression is that we can perform an F-test of the joint significance of the lagged inflation, interest rates, and unemployment rates in predicting forecast errors. In each case the macroeconomic data are overwhelmingly jointly statistically significant, suggesting that median inflation expectations do not adequately account for recent available information. Note that these findings do not depend on whether we condition on the forecast of inflation. Ball and Croushore (2003) interpret the estimated coefficients in a regression similar to that in panel D as capturing the extent to which agents under- or overreact to information. For instance, under the implicit assumption that, in the data, high inflation this period will tend to be followed by high inflation in the next period, the finding that the coefficient on inflation in panel D is positive implies that agents have underreacted to the recent inflation news. Our data support this conclusion in three of the four regressions (the Michigan series is the exception). Similarly, a high nominal interest rate today could signal lower inflation tomorrow because it indicates contractionary monetary policy by the Central Bank. We find that forecasts appear to underreact to short-term interest rates in all four regressions—high interest rates lead forecasters to make negative forecast errors or to predict future inflation that is too high. Finally, if in the economy a period of higher unemployment is usually followed by lower inflation (as found in estimates of the Phillips curve), then a negative coefficient on unemployment in panel D would indicate that agents are overestimating inflation following a rise in unemployment and thus are underreacting to the news in higher unemployment. We find that inflation expectations of economists are indeed too high during periods of high unemployment, again suggesting a pattern of underreaction; this is an error not shared by consumers. Our results are in line with Ball and Croushore's (2003) finding that agents seem to underreact to information when forming their expectations of inflation. In sum, Table 4 suggests that each of these data series alternatively meets and fails some of the implications of rationality. Our sense is that


these results probably capture the general flavor of the existing empirical literature, if not the somewhat stronger arguments made by individual authors. Bias exists but is typically small. Forecasts are typically inefficient, though not in all surveys: while the forecast errors of economists are not predictable based merely on their forecasts, those of consumers are. All four data series show substantial evidence that forecast errors made a year ago continue to repeat themselves, and that recent macroeconomic data is not adequately reflected in inflation expectations. We now turn to analyzing whether the data are consistent with adaptive expectations, probably the most popular alternative to rational expectations in the literature. The simplest backward-looking rule invokes the prediction that expected inflation over the next year will be equal to inflation over the past year. Ball (2000) suggests a stronger version, whereby agents form statistically optimal univariate inflation forecasts. The test in Table 5 is a little less structured, simply regressing median inflation expectations against the last eight nonoverlapping, three-month-ended inflation observations. We add the unemployment rate and short-term interest rates to this regression, finding that these macroeconomic aggregates also help predict inflation expectations. In particular, it is clear that when the unemployment rate rises over the quarter, inflation expectations fall further than adaptive expectations might suggest. This suggests that consumers employ a more sophisticated model of the economy than assumed in the simple adaptive expectations model. Consequently we are left with a somewhat negative result—observed inflation expectations are consistent with neither the sophistication of rational expectations nor the naivete of adaptive expectations. This finding holds for our four datasets, and it offers a reasonable interpretation of the prior literature on inflation expectations. The common thread to these results is that inflation expectations reflect partial and incomplete updating in response to macroeconomic news. We shall argue in Section 5 that these results are consistent with models in which expectations are not updated at every instant, but rather in which updating occurs in a staggered fashion. A key implication is that disagreement will vary with macroeconomic conditions.

4. Dispersion in Survey Measures of Inflation Expectations Few papers have explored the features of the cross-sectional variation in inflation expectations. Bryan and Venkatu (2001) examine a survey of inflation expectations in Ohio from 1998-2001, finding that women, singles, nonwhites, high school dropouts, and lower income groups tend to have higher inflation expectations than other demographic groups. They

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plus two measures of excess capacity: an output gap constructed as the difference between the natural logs of actual chain-weighted real output and trend output (constructed from a Hodrick-Prescott filter). The shaded regions represent periods of economic expansion and contraction as marked by the National Bureau of Economic Research (NBER) Business Cycle Dating Committee.8 The series on disagreement among consumers appears to rise during recessions, at least through the second half of the sample. A much weaker relationship is observed through the first half of the sample. Disagreement among economists shows a less obvious relationship with the state of the real economy. The final set of data that we examine can be thought of as either a cause or consequence of disagreement in inflation expectations. We consider the dispersion in actual price changes across different CPI categories. That is, just as Bryan and Cecchetti (1994) produce a weighted median CPI by calculating rates of inflation across 36 commodity groups, we construct a weighted interquartile range of year-ended inflation rates across 8. We have also experimented using the unemployment rate as a measure of real activity and obtained similar results.

226 • MANKIW, REIS, & WOLFERS commodity groups. One could consider this a measure of the extent to which relative prices are changing. We analyze data for the period December 1967-December 1997 provided by the Cleveland Fed. Figure 8 shows the median inflation rate and the 25th and 75th percentiles of the distribution of nominal price changes. Dispersion in commodity-level rates of inflation seems to rise during periods in which the dispersion in inflation expectations rises. In Figure 9, we confirm this, graphing this measure of dispersion in rates of price change against our measures of dispersion in expectations. The two look to be quite closely related. Table 6 considers each of the factors discussed above simultaneously, reporting regressions of the level of disagreement against inflation, the squared change in inflation, the output gap, and the dispersion in different commodities' actual inflation rates. Across the four table columns, we tend to find larger coefficients in the regressions focusing on consumer expectations than in those of economists. This reflects the differences in the extent of disagreement, and how much it varies over the cycle, across these populations. In both bivariate and multivariate regressions, we find the inflation rate to be an extremely robust predictor of disagreement. The squared change Figure 7 DISAGREEMENT AND THE REAL ECONOMY Disagreement Among Consumers

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0

2.0-.4 Michigan (smoothed)

Michigan - Experimental (smoothed)

Output Gap (RHS) --6

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% 4.0-

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SPF (smoothed) 1960

1970

1980 Year

Shaded areas denoted NBER-dated recessions

1990

2000

Figure 8 DISTRIBUTION OF INFLATION RATES ACROSS CPI COMPONENTS Weighted Percentiles, Based on 36 CPI Component Indices 25th Percentile Inflation Rate 75th Percentile Inflation Rate IQR of Weighted Component-Level Inflation Rates over Past Year

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15

228 • MANKIW, REIS, & WOLFERS Table 6 DISAGREEMENT AND THE BUSINESS CYCLE: ESTABLISHING STYLIZED FACTS1 Michigan

Michiganexperimental

Livingston

SPF (GDP deflator)

I represents a separate regression) Panel A: bivariate regressions (each cell

Inflation rate AInflation-squared Output gap Relative price variability

0.441*** (0.028) 18.227*** (2.920) 0.176 (0.237) 0.665*** (0.056)

0.228*** (0.036) 1.259** (0.616) -0.047 (0.092) 0.473*** (0.091)

0.083*** (0.016) 2.682*** (0.429) 0.070** (0.035) 0.117** (0.046)

0.092*** (0.013) 2.292** (0.084) -0.001 (0.029) 0.132 (0.016)

Panel B: regressions controlling for the inflation rate ([each cell represents a separate regression)

AInflation-squared Output gap Relative price variability

10.401*** (1.622) 0.415*** (0.088) 0.268*** (0.092)

0.814 (0.607) 0.026 (0.086) 0.210 (0.135)

2.051*** (0.483) -0.062** (0.027) 0.085** (0.042)

-0.406 (0.641) -0.009 (0.013) 0.099*** (0.020)

0.066*** (0.013) 1.663** (0.737) 0.020 (0.032)

0.095*** (0.015) -0.305 (0.676) -0.007 (0.014)

Panel C: multivariate regressions (full sample)

Inflation rate AInflation-squared Output gap

0.408*** (0.028) 7.062*** (1.364) 0.293*** (0.066)

0.217*** (0.034) 0.789 (0.598) 0.017 (0.079)

Panel D: multivariate regressions (including inflation dispersion)

Inflation rate AInflation-squared Output gap Relative price variability

0.328*** (0.034) 5.558*** (1.309) 0.336*** (0.067) 0.237*** (0.079)

0.204*** (0.074) -0.320 (2.431) -0.061 (0.117) 0.210 (0.159)

0.044** (0.018) 1.398 (0.949) 0.013 (0.039) 0.062 (0.038)

0.037*** (0.011) -0.411 (0.624) 0.006 (0.018) 0.100*** (0.022)

1. *** and ** denote statistical significance at the 1% and 5% levels, respectively (Newey-West standard errors in parentheses; correcting for autocorrelation up to one year).


in inflation is highly correlated with disagreement in bivariate regressions, and controlling for the inflation rate and other macroeconomic variables only slightly weakens this effect. Adding the relative price variability term further weakens this effect. Relative price variability is a consistently strong predictor of disagreement across all specifications. These results are generally stronger for the actual Michigan data than for the experimental series, and they are generally stronger for the Livingston series than for the SPF. We suspect that both facts reflect the relative role of measurement error. Finally, while the output gap appears to be related to disagreement in certain series, this finding is not robust either across data series or to the inclusion of controls. In sum, our analysis of the disagreement data has estimated that disagreement about the future path of inflation tends to: • Rise with inflation. • Rise when inflation changes sharply—in either direction. • Rise in concert with dispersion in rates of inflation across commodity groups. • Show no clear relationship with measures of real activity. Finally, we end this section with a note of caution. None of these findings necessarily reflect causality and, in any case, we have deliberately been quite loose in even speaking about the direction of likely causation. However, we believe that these findings present a useful set of stylized facts that a theory of macroeconomic dynamics should aim to explain.

5. Theories of Disagreement Most theories in macroeconomics have no disagreement among agents. It is assumed that everyone shares the same information and that all are endowed with the same information-processing technology. Consequently, everyone ends up with the same expectations. A famous exception is the islands model of Robert Lucas (1973). Producers are assumed to live in separate islands and to specialize in producing a single good. The relative price for each good differs by islandspecific shocks. At a given point in time, producers can observe the price only on their given islands and from it, they must infer how much of it is idiosyncratic to their product and how much reflects the general price level that is common to all islands. Because agents have different information, they have different forecasts of prices and hence inflation. Since all will inevitably make forecast errors, unanticipated monetary policy affects real output: following a change in the money supply, producers attribute some

230 • MANKIW, REIS, & WOLFERS of the observed change in the price for their product to changes in relative rather than general prices and react by changing production. This model relies on disagreement among agents and predicts dispersion in inflation expectations, as we observe in the data. Nonetheless, the extent of this disagreement is given exogenously by the parameters of the model. Although the Lucas model has heterogeneity in inflation expectations, the extent of disagreement is constant and unrelated to any macroeconomic variables. It cannot account for the systematic relationship between dispersion of expectations and macroeconomic conditions that we documented in Section 4. The sticky-information model of Mankiw and Reis (2002) generates disagreement in expectations that is endogenous to the model and correlated with aggregate variables. In this model, the costs of acquiring and processing information and of reoptimizing lead agents to update their information sets and expectations sporadically. Each period, only a fraction of the population update themselves on the current state of the economy and determine their optimal actions, taking into account the likely delay until they revisit their plans. The rest of the population continues to act according to their pre-existing plans based on old information. This theory generates heterogeneity in expectations because different segments of the population will have updated their expectations at different points in time. The evolution of the state of the economy over time will endogenously determine the extent of this disagreement. This disagreement in turn affects agents' actions and the resulting equilibrium evolution of the economy. We conducted the following experiment to assess whether the stickyinformation model can capture the extent of disagreement in the survey data. To generate rational forecasts from the perspective of different points in time, we estimated a vector autoregression (VAR) on U.S. monthly data. The VAR included three variables: monthly inflation (measured by the CPI), the interest rate on three-month Treasury bills, and a measure of the output gap obtained by using the Hodrick-Prescott filter on interpolated quarterly real GDP.9 The estimation period was from March 1947 to March 2002, and the regressions included 12 lags of each variable. We take this estimated VAR as an approximation to the model rational agents use to form their forecasts. We follow Mankiw and Reis (2002) and assume that in each period, a fraction \ of the population obtains new information about the state of the economy and recomputes optimal expectations based on this new information. Each person has the same probability of updating their informa9. Using employment rather than detrended GDP as the measure of real activity leads to essentially the same results.


tion, regardless of how long it has been since the last update. The VAR is then used to produce estimates of future annual inflation in the United States given information at different points in the past. To each of these forecasts, we attribute a frequency as dictated by the process just described. This generates at each point in time a full cross-sectional distribution of annual inflation expectations. We use the predictions from 1954 onward, discarding the first few years in the sample when there are not enough past observations to produce nondegenerate distributions. We compare the predicted distribution of inflation expectations by the sticky-information model to the distribution we observe in the survey data. To do so meaningfully, we need a relatively long sample period. This leads us to focus on the Livingston and the Michigan experimental series, which are available for the entire postwar period. The parameter governing the rate of information updating in the economy, X, is chosen to maximize the correlation between the interquartile range of inflation expectations in the survey data with that predicted by the model. For the Livingston Survey, the optimal X is 0.10, implying that the professional economists surveyed are updating their expectations about every 10 months, on average. For the Michigan series, the value of X that maximizes the correlation between predicted and actual dispersion is 0.08, implying that the general public updates their expectations on average every 12.5 months. These estimates are in line with those obtained by Mankiw and Reis (2003), Carroll (2003a), and Khan and Zhu (2002). These authors employ different identification schemes and estimate that agents update their information sets once a year, on average. Our estimates are also consistent with the reasonable expectation that people in the general public update their information less frequently than professional economists do. It is more surprising that the difference between the two is so small. A first test of the model is to see to what extent it can predict the dispersion in expectations over time. Figure 10 plots the evolution of the interquartile range predicted by the sticky-information model, given the history of macroeconomic shocks and VAR-type updating, and setting X = 0.1. The predicted interquartile range matches the key features of the Livingston data closely, and the two series appear to move closely together. The correlation between them is 0.66. The model is also successful at matching the absolute level of disagreement. While it overpredicts dispersion, it does so only by 0.18 percentage points on average. The sticky-information model also predicts the time-series movement in disagreement among consumers. The correlation between the predicted and actual series is 0.80 for the actual Michigan data and 0.40 for the longer experimental series. As for the level of dispersion, it is 4 percentage points

232 • MANKIW, REIS, & WOLFERS Figure 10 ACTUAL AND PREDICTED DISPERSION OF INFLATION EXPECTATIONS 12-

^ ^ ^ ™ " ^ ~ Predicted: Sticky-Information Model

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higher on average in the data than predicted by the model. This may be partially accounted for by some measurement error in the construction of the Michigan series. More likely, however, it reflects idiosyncratic heterogeneity in the population that is not captured by the model. Individuals in the public probably differ in their sources of information, in their sophistication in making forecasts, or even in their commitment to truthful reporting in a survey. None of these sources of individual-level variation are captured by the sticky-information model, but they might cause the high levels of disagreement observed in the data.10 Section 4 outlined several stylized facts regarding the dispersion of inflation expectations in the survey data. The interquartile range of expected inflation was found to rise with inflation and with the squared change in annual inflation over the last year. The output gap did not seem to affect significantly the dispersion of inflation expectations. We reestimate the regressions in panels A and C of Table 6, now using as the 10. An interesting illustration of this heterogeneity is provided by Bryan and Ventaku (2001), who find that men and women in the Michigan Survey have statistically significant different expectations of inflation. Needless to say, the sticky-information model does not incorporate gender heterogeneity.


Table 7 MODEL-GENERATED DISAGREEMENT AND MACROECONOMIC CONDITIONS1 Multivariate regression

Bivariate regressions

Dependent Variable: Interquartile range of model-generated inflation expectations

Constant Inflation rate AInflation-squared Output gap Adjusted R2 N

0.005*** (0.001) 0.127*** (0.028) 3.581*** (0.928) 0.009 (0.051) 0.469 579

0.166*** (0.027) 6.702*** (1.389) 0.018 (0.080) 579

I. *** denotes statistical significance at the 1% level (Newey-West standard errors in parentheses; correcting for autocorrelation up to one year).

dependent variable the dispersion in inflation expectations predicted by the sticky-information model with a A of 0.1, the value we estimated using the Livingston series.11 Table 7 presents the results. Comparing Table 7 with Table 6, we see that the dispersion of inflation expectations predicted by the sticky-information model has essentially the same properties as the actual dispersion of expectations we find in the survey data. As is true in survey data, the dispersion in sticky-information expectations is also higher when inflation is high, and it is higher when prices have changed sharply. As with the survey data, the output gap does not have a statistically significant effect on the model-generated dispersion of inflation expectations.12 We can also see whether the model is successful at predicting the central tendency of expectations, not just dispersion. Figure 11 plots the median expected inflation, both in the Livingston and Michigan surveys and as predicted by the sticky-information model with A = 0.1. The Livingston and predicted series move closely with each other: the correlation is 0.87. The model slightly overpredicts the data between 1955 and II. Using instead the value of A, that gave the best fit with the Michigan series (0.08) gives similar results. 12. The sticky-information model can also replicate the stylized fact from Section 5 that more disagreement comes with larger relative price dispersion. Indeed, in the sticky-information model, different price-setters choose different prices only insofar as they disagree on their expectations. This is transparent in Ball, Mankiw, and Reis (2003), where it is shown that relative price variability in the sticky-information model is a weighted sum of the squared deviations of the price level from the levels expected at all past dates, with earlier expectations receiving smaller weights. In the context of the experiment in this section, including relative price dispersion as an explanatory variable for the disagreement of inflation expectations would risk confounding consequences of disagreement with its driving forces.

234 • MANKIW, REIS, & WOLFERS 1965, and it underpredicts median expected inflation between 1975 and 1980. On average these two effects cancel out, so that over the whole sample, the model approximately matches the level of expected inflation (it overpredicts it by 0.3%). The correlation coefficient between the predicted and the Michigan experimental series is 0.49, and on average the model matches the level of median inflation expectations, underpredicting it by only 0.5%. In Section 3, we studied the properties of the median inflation expectations across the different surveys, finding that these data were consistent with weaker but not stronger tests of rationality. Table 8 is the counterpart to Table 4, using as the dependent variable the median expected inflation series generated by the sticky-information model. Again, these results match the data closely. We cannot reject the hypothesis that expectations are unbiased and efficient in the weak sense of panels A and B. Recall that, in the data, we found mixed evidence regarding these tests. Panels C and D suggest that forecasting errors in the sticky-information expectations are persistent and do not fully incorporate macroeconomic data, just as we found to be consistently true in the survey data. Table 9 offers the counterpart to Table 5, testing whether expectations can be described as purely adaptive. This hypothesis is strongly rejected—sticky-information expectations are much more rational than Figure 11 ACTUAL AND PREDICTED MEDIAN INFLATION EXPECTATIONS 12-

Predicted: Sticky-Information Model

Actual: Michigan

Actual: Livingston

Actual: Michigan Experimental

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Disagreement About Inflation Expectations • 235 Table 8 TESTS OF FORECAST RATIONALITY: MEDIAN INFLATION EXPECTATIONS PREDICTED BY THE STICKYINFORMATION MODEL 1 Panel A: Testing for bias: n, - Et_n nt = a Mean error (Constant only)

0.262% (0.310)

Panel B: Is information in the forecast fully exploited? nt - E,_12 izt = a + p

p: E M 2 [TCJ

0.436* (0.261) -1.416%* (0.822) 0.088 No p = 0.227

a: constant Adj. R2 Reject efficiency? a = (3 = 0

Panel C: Are forecasting errors persistent? nt - Et_12 K, = a + (3 (nt_u - Et_24 0

ICf-12 - Ef-24 ["l-lJ

- 6 0 4 ***

(0.124) 0.107% (0.211) 0.361

Constant Adj. R2

Panel D: Are macroeconomic data fully exploited? nt - £f_12 nt = a + E(-12 M

+ 1 Jtf-13 +

K

a: constant P: E M 2 [TCJ 7: inflation,

13

K: Treasury t>illf_13 5: unemployment,..^ Reject efficiency? y=K = 8 = 0 Adjusted R2

h-U + 5 LJt-13

1.567%* (0.824) 0.398 (0.329) 0.506*** (0.117) -0.413** (0.139) -0.450*** (0.135) Yes p = 0.000 0.369

1. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively (Newey-West standard errors in parentheses; correcting for autocorrelation up to one year).

236 • MANKIW, REIS, & WOLFERS

simple, backward-looking adaptive expectations. Again, this finding matches what we observed in the survey data. Given how closely the predicted and actual dispersion of expectations and median expected inflation co-move, it is not surprising to find that the results in Tables 4, 5, and 6 are closely matched by the model-generated time series for disagreement in Tables 7,8, and 9. A stronger test in the tradition of moment-matching is to see whether the sticky-information model can robustly generate the stylized facts we observe in the data. We verify this by implementing the following exercise. Using the residuals from our estimated VAR as an empirical distribution, we randomly draw 720 residual vectors and, using the VAR parameter estimates, use these draws to build hypothetical series for inflation, the output gap, and the Treasury-bill rate. We then employ the sticky-information model to generate a predicted distribution of inflation expectations at each date, using the procedure outlined earlier. To eliminate the influence of initial conditions, we discard the first 10 years of the simulated series so that we are left with 50 years of simulated data. We repeat this procedure 500 times, thereby generating 500 alternative 50-year histories for inflation, the output gap, the Treasury-bill rate, the median expected inflation, and the interquartile range of inflation expectations predicted by the sticky-information model with A, = 0.1. The regressions in Tables 4, 5, and 6, describing the relationship of disagreement and forecast errors Table 9 TESTS OF ADAPTIVE EXPECTATIONS: MEDIAN INFLATION EXPECTATIONS PREDICTED BY THE STICKYINFORMATION MODEL1 Adaptive expectations: Etnt+U - a + p(X) nt + y Ut + K U,_3 + 5 i, +